1) The NYC Crime map shows how many and what types of crimes occurred throughout the city. You can look by precinct, by graduated point map (which shows how many crimes occurred in a specific spot that you can drill down by zooming in), and by heat map (where changing colors indicate a larger number of crimes). You can even specify which kinds of crimes you would like to see information for.
One thing you won't see too much of is murder. Thankfully, as former Mayor Bloomberg pointed out, NYC has had very few violent crimes given how large the city is over the past few years. This tool is great for people moving to the city who want to understand what happens in different neighborhoods, and residents who what to keep track of what is happening in their particular area.
2) The NYC Business Atlas shows a variety of demographic information about population and business density. It shows businesses by heat maps and also the number of different types of businesses in a specific area, as well as what types of businesses have started up recently. Prospective residents might find this information useful as they evaluate various neighborhoods. http://maps.nyc.gov/businessatlas/